{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "import argparse\n",
    "import copy\n",
    "import json\n",
    "import os\n",
    "import pickle\n",
    "import random\n",
    "import sys\n",
    "import re\n",
    "import numpy as np\n",
    "import openai\n",
    "\n",
    "sys.path.append('C:\\\\Users\\\\Pluto\\\\Desktop\\\\TaDe')\n",
    "from utils import *\n",
    "\n",
    "os.environ[\"http_proxy\"] = \"http://localhost:7890\"\n",
    "os.environ[\"https_proxy\"] = \"http://localhost:7890\"\n",
    "\n",
    "GPT_MODEL = \"gpt-4-turbo\"  # [gpt-4-turbo-preview]\n",
    "\n",
    "setOpenAi(keyid = 3)\n",
    "\n",
    "with open(\"puzzles.json\", \"r\") as f:\n",
    "    puzzles = json.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'name': 'TripleZeroSum:2', 'sat': 'def sat(inds: List[int], nums=[-64, -74, -18, -57, 89, -14, -25, 11, -60, -78]):\\n    return len(inds) == 3 and sum(nums[i] for i in inds) == 0', 'ans_type': 'List[int]', 'sol_header': 'def sol(nums=[-64, -74, -18, -57, 89, -14, -25, 11, -60, -78]):', 'sol_docstring': '    \"\"\"\\n    Find the indices of three numbers that sum to 0 in a list.\\n\\n    --- Example input ---\\n    [1, 2, 4, -3, 5]\\n\\n    --- Example output ---\\n    [0, 1, 3]\\n    \"\"\"', 'sol_bodies': ['    # \\\\tilde{O}(n^2) algorithm\\n    inv = {n: i for i, n in enumerate(nums)}  # note that later duplicates will override earlier entries\\n    for i, n in enumerate(nums):\\n        if inv[n] == i:\\n            del inv[n]\\n        if any((-m - n) in inv for m in nums[:i]):  # found solution!\\n            j, m = next((j, m) for j, m in enumerate(nums) if (-m - n) in inv)\\n            k = inv[-m - n]\\n            return sorted([i, j, k])'], 'module': 'human_eval.py', 'notes': 'Inspired by [HumanEval](https://github.com/openai/human-eval) \\\\#40\\n    \\nSimilar to but harder than PairZeroSum \\\\#43.\\n    \\nThis is a version of the classic [3SUM](https://en.wikipedia.org/wiki/3SUM) problem.', 'weight': 1.0}\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "# 随机选择一个puzzle进行解决\n",
    "i = random.randint(0, len(puzzles))\n",
    "question = puzzles[i]['sat']\n",
    "print(puzzles[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decompose_sql(question):    \n",
    "    \n",
    "    question_example = f\"\"\"\n",
    "You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\n",
    "Here is the puzzle: \n",
    "def sat(start: int, k=1, lower=93, seq=[-61, -46, 89, 93, -13, 14, -95, -74, -92, -38, -93, 64, -78, 3, 92, -10, -4, 43, 72, 12, 3, -3, -15, -96, 72, -71, -30, 53, 17, -87, 49, 17, -69, 78, 6, -77, -99, 91, 13, 9, 81, -55, 75, 48, -65, 18, -83, 10, -12, 88, 60, -72, -7, -49, -56, -76, 82, 18, 77, 52, -92, -88, 39, 13, -16, 82, 4, 44, -19, 54, 6, 55, 77, -38, -30, -55, -16]):\n",
    "    return 0 <= start <= len(seq) - k and sum(seq[start:start + k]) >= lower\n",
    "    \n",
    "You have to decompose the puzzle into multiple steps. Carefully consider the granularity of each subtask to ensure that each one is executable.\n",
    "\n",
    "Answer format: Please follow the format below strictly when answering. No explanation is required.\n",
    "STEP1 [ step task 1 ]\n",
    "STEP2 [ step task 2 ]\n",
    "...\n",
    "\"\"\"\n",
    "    answer_example = f\"\"\"\n",
    "STEP1 [ Understand the puzzle's primary objective: Find an integer 'start' such that when added to the subsequent 'k' elements in 'seq', the sum is greater than or equal to 'lower'. ]\n",
    "STEP2 [ Note the inputs: 'k', 'lower', and 'seq' are given and fixed. ]\n",
    "STEP3 [ Recognize the constraints: The variable 'start' must be within the range 0 to len(seq) - k. ]\n",
    "STEP4 [ Comprehend that sum(seq[start:start + k]) needs to be greater than or equal to 'lower'. ]\n",
    "STEP5 [ Deduce a strategy: Loop through the sequence from 0 to len(seq) - k to find a valid 'start'. ]\n",
    "STEP6 [ For each 'start' value in the loop, calculate sum(seq[start:start + k]). ]\n",
    "STEP7 [ Compare the calculated sum with 'lower'. ]\n",
    "STEP8 [ If the sum is greater than or equal to 'lower', return that 'start' value. ]\n",
    "\"\"\"\n",
    "\n",
    "    Example = [\n",
    "        {\"role\": \"user\", \"content\": question_example},\n",
    "        {\"role\": \"assistant\", \"content\": answer_example}\n",
    "    ]\n",
    "\n",
    "\n",
    "    prompt_for_decompose = f\"\"\"\n",
    "You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\n",
    "Here is the puzzle: {question}\n",
    "You have to decompose the puzzle into multiple steps. Carefully consider the granularity of each subtask to ensure that each one is executable.\n",
    "\n",
    "Answer format: Please follow the format below strictly when answering. No explanation is required.\n",
    "STEP1 [ step task 1 ]\n",
    "STEP2 [ step task 2 ]\n",
    "...\n",
    "\"\"\"\n",
    "    Q = {\n",
    "        \"role\": \"user\",\n",
    "        \"content\": prompt_for_decompose\n",
    "    }\n",
    "    Query = Example+[Q]\n",
    "    result = askChatGPT(Query, model=GPT_MODEL, temperature=1)\n",
    "    return result\n",
    "\n",
    "\n",
    "def convert_steps_to_format(raw_steps):\n",
    "    lines = raw_steps.strip().split('\\n')\n",
    "    steps_dict = {}\n",
    "    steps = []\n",
    "    for line in lines:\n",
    "        if line.strip():  # 只处理非空行\n",
    "            step_number = int(line.split(' ')[0][4:])  # 提取数值部分并转换为整数\n",
    "            step_id = line.split(' ')[0]\n",
    "            step_content = line[line.index('[') + 1 : line.rindex(']')]\n",
    "            steps_dict[step_number] = step_content\n",
    "            steps.append({\"stepId\": step_number, \"step\": step_content})\n",
    "            \n",
    "            \n",
    "    # return steps_dict\n",
    "    return steps, steps_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "STEP1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ]\n",
      "STEP2 [ Note the inputs: 'nums' is a given and fixed list. ]\n",
      "STEP3 [ Recognize constraints: 'inds' must have exactly 3 elements. ]\n",
      "STEP4 [ Comprehend that the sum of nums at those indices must equal 0. ]\n",
      "STEP5 [ Consider all possible combinations of 3 indices in 'nums'. ]\n",
      "STEP6 [ For each combination of indices, calculate the sum of values at those indices. ]\n",
      "STEP7 [ Check if the calculated sum equals 0. ]\n",
      "STEP8 [ If a valid set of indices is found, return them. ]\n"
     ]
    }
   ],
   "source": [
    "result = decompose_sql(question)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'stepId': 1, 'step': \" Understand the objective: Find three indices in 'nums' whose values sum up to 0. \"}, {'stepId': 2, 'step': \" Note the inputs: 'nums' is a given and fixed list. \"}, {'stepId': 3, 'step': \" Recognize constraints: 'inds' must have exactly 3 elements. \"}, {'stepId': 4, 'step': ' Comprehend that the sum of nums at those indices must equal 0. '}, {'stepId': 5, 'step': \" Consider all possible combinations of 3 indices in 'nums'. \"}, {'stepId': 6, 'step': ' For each combination of indices, calculate the sum of values at those indices. '}, {'stepId': 7, 'step': ' Check if the calculated sum equals 0. '}, {'stepId': 8, 'step': ' If a valid set of indices is found, return them. '}]\n"
     ]
    }
   ],
   "source": [
    "steps, steps_dict = convert_steps_to_format(result)\n",
    "print(steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "建图→化简→可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ipydagred3\n",
    "import networkx as nx\n",
    "\n",
    "def construct_dependencies_without_traversal(question, steps):\n",
    "    prompt = f\"Now Given the following subtasks for question: {question}, determine the dependencies between them:\\n\"\n",
    "    for step in steps:\n",
    "        prompt += f\"Step {step['stepId']}: {step['step']}\\n\"\n",
    "    prompt += \"\"\"\\nPlease list the dependencies in the format 'Subtask A [xxx] -> Subtask B [xxx]' indicating that Subtask A must be completed before Subtask B can start.\n",
    "Please identify any potential conditional dependencies from a logical perspective.\n",
    "\n",
    "Answer format: (Please strictly follow the format. Each dependency should be separated by a new line. No explanation is required.)\n",
    "Step id_i [  subtask i ] -> Step id_j [ subtask j ]\n",
    "Step id_m [  subtask m ] -> Step id_n [ subtask n ]\n",
    "...\n",
    "\"\"\"\n",
    "    prompt_user = {\n",
    "        \"role\": \"user\",\n",
    "        \"content\": f\"\"\"{prompt}\"\"\"\n",
    "    }\n",
    "    Query = [prompt_user]\n",
    "    output = askChatGPT(Query, model=GPT_MODEL, temperature=1)\n",
    "    return output\n",
    "\n",
    "def create_dag_from_string(dependencies_string):\n",
    "    G = nx.DiGraph()\n",
    "    \n",
    "    # Split the string by newlines to get individual dependencies\n",
    "    dependencies = dependencies_string.strip().split('\\n')\n",
    "    \n",
    "    for dependency in dependencies:\n",
    "        # Split each dependency by the arrow\n",
    "        steps = dependency.split(' -> ')\n",
    "        if len(steps) == 2:\n",
    "            step_0 = steps[0].strip()\n",
    "            step_1 = steps[1].strip()\n",
    "            # Add edges based on dependencies\n",
    "            G.add_edge(step_0, step_1)\n",
    "    \n",
    "    # Print the edges\n",
    "    # print(list(G.edges()))\n",
    "    # Perform transitive reduction to simplify the graph\n",
    "    transitive_reduction = nx.transitive_reduction(G)\n",
    "    return transitive_reduction\n",
    "\n",
    "def create_graph(reduced_dependencies, problem):\n",
    "    graph = ipydagred3.Graph()\n",
    "\n",
    "    #for state in steps_list:\n",
    "    #    graph.setNode(state, tooltip='tooltip1 of ' + state)\n",
    "        \n",
    "    for dependency in reduced_dependencies:\n",
    "        graph.setEdge(*dependency)\n",
    "\n",
    "    graph.setNode(problem, tooltip = \"Problem Statement\")\n",
    "        \n",
    "    widge_try = ipydagred3.DagreD3Widget(graph=graph)\n",
    "    \n",
    "    return widge_try"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Step 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ] -> Step 2 [ Note the inputs: 'nums' is a given and fixed list. ]\\nStep 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ] -> Step 3 [ Recognize constraints: 'inds' must have exactly 3 elements. ]\\nStep 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ] -> Step 4 [ Comprehend that the sum of nums at those indices must equal 0. ]\\nStep 2 [ Note the inputs: 'nums' is a given and fixed list. ] -> Step 5 [ Consider all possible combinations of 3 indices in 'nums'. ]\\nStep 3 [ Recognize constraints: 'inds' must have exactly 3 elements. ] -> Step 6 [ For each combination of indices, calculate the sum of values at those indices. ]\\nStep 4 [ Comprehend that the sum of nums at those indices must equal 0. ] -> Step 7 [ Check if the calculated sum equals 0. ]\\nStep 5 [ Consider all possible combinations of 3 indices in 'nums'. ] -> Step 6 [ For each combination of indices, calculate the sum of values at those indices. ]\\nStep 6 [ For each combination of indices, calculate the sum of values at those indices. ] -> Step 7 [ Check if the calculated sum equals 0. ]\\nStep 7 [ Check if the calculated sum equals 0. ] -> Step 8 [ If a valid set of indices is found, return them. ]\""
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relations_test = construct_dependencies_without_traversal(question, steps)  # query LLM回答所有的依赖\n",
    "relations_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(\"Step 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ]\", \"Step 2 [ Note the inputs: 'nums' is a given and fixed list. ]\"), (\"Step 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ]\", 'Step 4 [ Comprehend that the sum of nums at those indices must equal 0. ]'), (\"Step 1 [ Understand the objective: Find three indices in 'nums' whose values sum up to 0. ]\", \"Step 3 [ Recognize constraints: 'inds' must have exactly 3 elements. ]\"), (\"Step 2 [ Note the inputs: 'nums' is a given and fixed list. ]\", \"Step 5 [ Consider all possible combinations of 3 indices in 'nums'. ]\"), (\"Step 3 [ Recognize constraints: 'inds' must have exactly 3 elements. ]\", 'Step 6 [ For each combination of indices, calculate the sum of values at those indices. ]'), ('Step 4 [ Comprehend that the sum of nums at those indices must equal 0. ]', 'Step 7 [ Check if the calculated sum equals 0. ]'), (\"Step 5 [ Consider all possible combinations of 3 indices in 'nums'. ]\", 'Step 6 [ For each combination of indices, calculate the sum of values at those indices. ]'), ('Step 6 [ For each combination of indices, calculate the sum of values at those indices. ]', 'Step 7 [ Check if the calculated sum equals 0. ]'), ('Step 7 [ Check if the calculated sum equals 0. ]', 'Step 8 [ If a valid set of indices is found, return them. ]')]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "82cdd1c5cf574754b5fdb2df3429c6e7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "DagreD3Widget()"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G1 = create_dag_from_string(relations_test)  # LLM 进行建图与化简\n",
    "reduced_dependencies = list(G1.edges())\n",
    "print(reduced_dependencies)\n",
    "create_graph(reduced_dependencies, question)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Step 1 [ Understand the objective ]', 'Step 3 [ Comprehend the condition to satisfy ]'), ('Step 3 [ Comprehend the condition to satisfy ]', 'Step 6 [ Adjust the computed square root if necessary ]'), (\"Step 2 [ Recognize input 'a' is given and fixed ]\", 'Step 5 [ Devise a strategy ]'), ('Step 5 [ Devise a strategy ]', 'Step 6 [ Adjust the computed square root if necessary ]'), ('Step 4 [ Recall mathematical knowledge ]', 'Step 5 [ Devise a strategy ]')]\n",
      "[('Step 1', 'Step 3'), ('Step 3', 'Step 6'), ('Step 2', 'Step 5'), ('Step 5', 'Step 6'), ('Step 4', 'Step 5')]\n",
      "[(1, 3), (3, 6), (2, 5), (5, 6), (4, 5)]\n"
     ]
    }
   ],
   "source": [
    "print(reduced_dependencies)\n",
    "# 进行一些化简\n",
    "edges = []\n",
    "for item in reduced_dependencies:\n",
    "    edges.append((item[0][:item[0].find('[')].strip(), item[1][:item[1].find('[')].strip()))\n",
    "print(edges)\n",
    "\n",
    "int_edges = [(int(e[0].split()[1]), int(e[1].split()[1])) for e in edges]\n",
    "print(int_edges)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "层级深度计算,似乎是对的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Step 4': 0, 'Step 1': 0, 'Step 2': 0, 'Step 3': 1, 'Step 5': 1, 'Step 6': 2}\n"
     ]
    }
   ],
   "source": [
    "# 计算节点的深度\n",
    "\n",
    "from collections import deque, defaultdict\n",
    "\n",
    "def calculate_node_depths(edges):\n",
    "    # 初始化节点的入度和邻接表\n",
    "    in_degree = defaultdict(int)\n",
    "    adjacency_list = defaultdict(list)\n",
    "    \n",
    "    nodes = set()\n",
    "    \n",
    "    # 填充邻接表和计算入度\n",
    "    for u, v in edges:\n",
    "        adjacency_list[u].append(v)\n",
    "        in_degree[v] += 1\n",
    "        nodes.add(u)\n",
    "        nodes.add(v)\n",
    "    \n",
    "    # 找到所有入度为0的节点\n",
    "    queue = deque([node for node in nodes if in_degree[node] == 0])\n",
    "    depth = {node: 0 for node in queue}\n",
    "    \n",
    "    # 广度优先搜索\n",
    "    while queue:\n",
    "        node = queue.popleft()\n",
    "        current_depth = depth[node]\n",
    "        \n",
    "        for neighbor in adjacency_list[node]:\n",
    "            in_degree[neighbor] -= 1\n",
    "            if in_degree[neighbor] == 0:\n",
    "                queue.append(neighbor)\n",
    "                depth[neighbor] = current_depth + 1\n",
    "    \n",
    "    return depth\n",
    "\n",
    "# 示例用法\n",
    "# edges = [(\"node1\", \"node2\"), (\"node1\", \"node3\"), (\"node2\", \"node4\"), (\"node3\", \"node4\"), (\"node4\", \"node5\")]\n",
    "node_depths = calculate_node_depths(edges)\n",
    "print(node_depths)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "开始基于图结构设计推理路径"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 首先推理所有深度为0的点\n",
    "import sys\n",
    "sys.path.append('C:\\\\Users\\\\Pluto\\\\Desktop\\\\TaDe')\n",
    "from utils import reverseDict, search_Predecessors\n",
    "\n",
    "# node_depths\n",
    "depths = reverseDict(node_depths)  # {0: ['Step 1'], 1: ['Step 3', 'Step 2'], 2: ['Step 5', 'Step 4'], 3: ['Step 6'], 4: ['Step 7'], 5: ['Step 8'], 6: ['Step 9']}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "def sat(x: float, a=7987622700):\n",
      "    return abs(x ** 2 - a) < 10 ** -3\n"
     ]
    }
   ],
   "source": [
    "print(question)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: \" Understand the objective: Find a float 'x' such that the difference between 'x' squared and 'a' is less than 0.001. \", 2: \" Recognize input 'a' is given and fixed. \", 3: ' Comprehend the condition to satisfy: abs(x ** 2 - a) < 10 ** -3. ', 4: \" Recall mathematical knowledge: 'x' is essentially the square root of 'a', within a small tolerance. \", 5: \" Devise a strategy: Compute the square root of 'a' as a starting point. \", 6: ' Adjust the computed square root if necessary to ensure the condition abs(x ** 2 - a) < 10 ** -3 is met. '}\n"
     ]
    }
   ],
   "source": [
    "print(steps_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Step 1', 'Step 3'), ('Step 3', 'Step 6'), ('Step 2', 'Step 5'), ('Step 5', 'Step 6'), ('Step 4', 'Step 5')]\n",
      "[(1, 3), (3, 6), (2, 5), (5, 6), (4, 5)]\n"
     ]
    }
   ],
   "source": [
    "print(edges)\n",
    "print(int_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "**********Question**********\n",
      "[{'role': 'system', 'content': 'You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\\nHere is the puzzle:\\ndef sat(x: float, a=7987622700):\\n    return abs(x ** 2 - a) < 10 ** -3\\nI have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\\nPlease follow the logical sequence of our subtasks to solve this problem.'}, {'role': 'user', 'content': \"\\nNow the subtask is:  Recall mathematical knowledge: 'x' is essentially the square root of 'a', within a small tolerance. \\nBased on the information above, please provide a concise and clear answer to this sub-task in one or two sentences..\"}]\n",
      "Answer: Given that 'x' is essentially the square root of 'a' within a small tolerance, to find an appropriate 'x', one needs to calculate the square root of 'a' (7987622700) and ensure the result is precise to within a very small margin, specifically less than 10^-3.\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "**********Question**********\n",
      "[{'role': 'system', 'content': 'You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\\nHere is the puzzle:\\ndef sat(x: float, a=7987622700):\\n    return abs(x ** 2 - a) < 10 ** -3\\nI have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\\nPlease follow the logical sequence of our subtasks to solve this problem.'}, {'role': 'user', 'content': \"\\nSo far, the answers to the resolved sub-tasks are as follows: The format is SubtaskId: xxx; Subtask: xxx; Answer: xxx.\\nSubtaskId: 4; Subtask:  Recall mathematical knowledge: 'x' is essentially the square root of 'a', within a small tolerance. ; Answer: Given that 'x' is essentially the square root of 'a' within a small tolerance, to find an appropriate 'x', one needs to calculate the square root of 'a' (7987622700) and ensure the result is precise to within a very small margin, specifically less than 10^-3.. Understand the objective: Find a float 'x' such that the difference between 'x' squared and 'a' is less than 0.001. \"}]\n",
      "Answer: Based on the insights provided from SubtaskId: 4, solving for 'x' involves calculating the square root of 'a' with a very high precision. The given value of 'a' is 7987622700. \n",
      "\n",
      "To find a float 'x' such that the difference between \\(x^2\\) and 'a' is less than \\(0.001\\), we aim to calculate the square root of 'a'. Essentially, we're seeking to identify \\(\\sqrt{7987622700}\\) with a precision that when squared, the absolute difference from 7987622700 is less than \\(10^{-3}\\).\n",
      "\n",
      "To calculate this:\n",
      "\n",
      "\\[x = \\sqrt{a} = \\sqrt{7987622700}\\]\n",
      "\n",
      "High precision calculation tools or programming languages functions that handle floating-point arithmetic with significant precision are required to ensure the difference criterion (\\(< 10^{-3}\\)) is met.\n",
      "\n",
      "Employing Python for this calculation as an example:\n",
      "\n",
      "```python\n",
      "import math\n",
      "x = math.sqrt(7987622700)\n",
      "```\n",
      "\n",
      "This calculation yields the value for 'x' we are looking for, ensuring it meets the specified tolerance when squared and compared to 'a'. Given the constraints outlined, it essentially means finding the square root of 7987622700 with a precision that ensures when 'x' is squared, it is within the range \\([7987622699.999, 7987622700.001]\\).\n",
      "\n",
      "Thus, calculating \\(\\sqrt{7987622700}\\) directly provides the solution to finding such an 'x' and concludes the logical follow-through based on the insights from the subtasks.\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "**********Question**********\n",
      "[{'role': 'system', 'content': 'You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\\nHere is the puzzle:\\ndef sat(x: float, a=7987622700):\\n    return abs(x ** 2 - a) < 10 ** -3\\nI have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\\nPlease follow the logical sequence of our subtasks to solve this problem.'}, {'role': 'user', 'content': \"\\nSo far, the answers to the resolved sub-tasks are as follows: The format is SubtaskId: xxx; Subtask: xxx; Answer: xxx.\\nSubtaskId: 4; Subtask:  Recall mathematical knowledge: 'x' is essentially the square root of 'a', within a small tolerance. ; Answer: Given that 'x' is essentially the square root of 'a' within a small tolerance, to find an appropriate 'x', one needs to calculate the square root of 'a' (7987622700) and ensure the result is precise to within a very small margin, specifically less than 10^-3..\\nSubtaskId: 1; Subtask:  Understand the objective: Find a float 'x' such that the difference between 'x' squared and 'a' is less than 0.001. ; Answer: Based on the insights provided from SubtaskId: 4, solving for 'x' involves calculating the square root of 'a' with a very high precision. The given value of 'a' is 7987622700. \\n\\nTo find a float 'x' such that the difference between \\\\(x^2\\\\) and 'a' is less than \\\\(0.001\\\\), we aim to calculate the square root of 'a'. Essentially, we're seeking to identify \\\\(\\\\sqrt{7987622700}\\\\) with a precision that when squared, the absolute difference from 7987622700 is less than \\\\(10^{-3}\\\\).\\n\\nTo calculate this:\\n\\n\\\\[x = \\\\sqrt{a} = \\\\sqrt{7987622700}\\\\]\\n\\nHigh precision calculation tools or programming languages functions that handle floating-point arithmetic with significant precision are required to ensure the difference criterion (\\\\(< 10^{-3}\\\\)) is met.\\n\\nEmploying Python for this calculation as an example:\\n\\n```python\\nimport math\\nx = math.sqrt(7987622700)\\n```\\n\\nThis calculation yields the value for 'x' we are looking for, ensuring it meets the specified tolerance when squared and compared to 'a'. Given the constraints outlined, it essentially means finding the square root of 7987622700 with a precision that ensures when 'x' is squared, it is within the range \\\\([7987622699.999, 7987622700.001]\\\\).\\n\\nThus, calculating \\\\(\\\\sqrt{7987622700}\\\\) directly provides the solution to finding such an 'x' and concludes the logical follow-through based on the insights from the subtasks.. Recognize input 'a' is given and fixed. \"}]\n",
      "Answer: To proceed with solving the provided puzzle programmatically, we use the Python code snippet from the discussion:\n",
      "\n",
      "```python\n",
      "import math\n",
      "\n",
      "# Calculation based on the provided logic\n",
      "a = 7987622700\n",
      "x = math.sqrt(a)\n",
      "\n",
      "# Verify if the solution meets the criteria\n",
      "solution = abs(x ** 2 - a) < 10 ** -3\n",
      "\n",
      "print(\"The solution is:\", x)\n",
      "print(\"Does the solution meet the criteria?\", solution)\n",
      "```\n",
      "\n",
      "By executing the Python code snippet, you calculate the square root of \\(7987622700\\) and verify if squaring this calculated value of 'x' and comparing it to 'a' falls within the specified tolerance (\\(< 0.001\\)). This direct application of calculating the square root as the solution to finding 'x' addresses the requirement set forth by the puzzle within the constraints of precision mentioned. Given this approach, the printed output will indicate the value of 'x' that solves the puzzle, alongside a boolean confirmation indicating whether or not the solution criteria have been met.\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "**********Question**********\n",
      "[{'role': 'system', 'content': 'You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\\nHere is the puzzle:\\ndef sat(x: float, a=7987622700):\\n    return abs(x ** 2 - a) < 10 ** -3\\nI have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\\nPlease follow the logical sequence of our subtasks to solve this problem.'}, {'role': 'user', 'content': '\\nSo far, the answers to the resolved sub-tasks are as follows: The format is SubtaskId: xxx; Subtask: xxx; Answer: xxx.\\nSubtaskId: 4; Subtask:  Recall mathematical knowledge: \\'x\\' is essentially the square root of \\'a\\', within a small tolerance. ; Answer: Given that \\'x\\' is essentially the square root of \\'a\\' within a small tolerance, to find an appropriate \\'x\\', one needs to calculate the square root of \\'a\\' (7987622700) and ensure the result is precise to within a very small margin, specifically less than 10^-3..\\nSubtaskId: 1; Subtask:  Understand the objective: Find a float \\'x\\' such that the difference between \\'x\\' squared and \\'a\\' is less than 0.001. ; Answer: Based on the insights provided from SubtaskId: 4, solving for \\'x\\' involves calculating the square root of \\'a\\' with a very high precision. The given value of \\'a\\' is 7987622700. \\n\\nTo find a float \\'x\\' such that the difference between \\\\(x^2\\\\) and \\'a\\' is less than \\\\(0.001\\\\), we aim to calculate the square root of \\'a\\'. Essentially, we\\'re seeking to identify \\\\(\\\\sqrt{7987622700}\\\\) with a precision that when squared, the absolute difference from 7987622700 is less than \\\\(10^{-3}\\\\).\\n\\nTo calculate this:\\n\\n\\\\[x = \\\\sqrt{a} = \\\\sqrt{7987622700}\\\\]\\n\\nHigh precision calculation tools or programming languages functions that handle floating-point arithmetic with significant precision are required to ensure the difference criterion (\\\\(< 10^{-3}\\\\)) is met.\\n\\nEmploying Python for this calculation as an example:\\n\\n```python\\nimport math\\nx = math.sqrt(7987622700)\\n```\\n\\nThis calculation yields the value for \\'x\\' we are looking for, ensuring it meets the specified tolerance when squared and compared to \\'a\\'. Given the constraints outlined, it essentially means finding the square root of 7987622700 with a precision that ensures when \\'x\\' is squared, it is within the range \\\\([7987622699.999, 7987622700.001]\\\\).\\n\\nThus, calculating \\\\(\\\\sqrt{7987622700}\\\\) directly provides the solution to finding such an \\'x\\' and concludes the logical follow-through based on the insights from the subtasks..\\nSubtaskId: 2; Subtask:  Recognize input \\'a\\' is given and fixed. ; Answer: To proceed with solving the provided puzzle programmatically, we use the Python code snippet from the discussion:\\n\\n```python\\nimport math\\n\\n# Calculation based on the provided logic\\na = 7987622700\\nx = math.sqrt(a)\\n\\n# Verify if the solution meets the criteria\\nsolution = abs(x ** 2 - a) < 10 ** -3\\n\\nprint(\"The solution is:\", x)\\nprint(\"Does the solution meet the criteria?\", solution)\\n```\\n\\nBy executing the Python code snippet, you calculate the square root of \\\\(7987622700\\\\) and verify if squaring this calculated value of \\'x\\' and comparing it to \\'a\\' falls within the specified tolerance (\\\\(< 0.001\\\\)). This direct application of calculating the square root as the solution to finding \\'x\\' addresses the requirement set forth by the puzzle within the constraints of precision mentioned. Given this approach, the printed output will indicate the value of \\'x\\' that solves the puzzle, alongside a boolean confirmation indicating whether or not the solution criteria have been met..\\nAmong them, sub-tasks [1] are directly related to this sub-task, so please pay special attention to them. Comprehend the condition to satisfy: abs(x ** 2 - a) < 10 ** -3. '}]\n",
      "Answer: With the information gathered from the previous subtasks, we understand that the primary goal is to find a value of `x` such that the absolute difference between `x` ** 2 and `a` is less than 0.001. The value `a` is given as 7987622700. Based on the mathematical and programming insights gained:\n",
      "\n",
      "1. The formula to find the suitable `x` boils down to calculating the square root of `a`, given the close approximation within a small tolerance (\\(<10^{-3}\\)).\n",
      "2. The calculated square root value of `a` needs to ensure that the squared result, when compared to `a`, fits within the tolerance specified.\n",
      "\n",
      "Following the steps outlined in the previous subtasks, `x` can be found using a square root function, preferably through a high-precision method or tool, such as Python's `math.sqrt` function. The solution from SubtaskId: 2 provides a practical blueprint for implementing this calculation and verifying the absolute difference criterion:\n",
      "\n",
      "```python\n",
      "import math\n",
      "\n",
      "# Calculation based on the provided logic\n",
      "a = 7987622700\n",
      "x = math.sqrt(a)\n",
      "\n",
      "# Verify if the solution meets the criteria\n",
      "solution = abs(x ** 2 - a) < 10 ** -3\n",
      "\n",
      "print(\"The solution is:\", x)\n",
      "print(\"Does the solution meet the criteria?\", solution)\n",
      "```\n",
      "\n",
      "When this code is executed,\n",
      "\n",
      "- It will calculate `x` as the square root of `a`, which directly addresses the given challenge.\n",
      "- It will then verify if this solution (`x`) meets the specific requirement: whether squaring this value (`x` squared) and then checking the absolute difference from `a` results in a value less than 0.001.\n",
      "\n",
      "Given that this calculation process and the subsequent verification align with the task's requirements, executing this code directly leads us to the solution, fulfilling the set criterion of `abs(x ** 2 - a) < 10 ** -3`. This comprehensive approach encapsulates the exploration and insights gathered from the previous subtasks, concluding the logical progression set out from the initial comprehension to the final implementation stage.\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "**********Question**********\n",
      "[{'role': 'system', 'content': 'You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\\nHere is the puzzle:\\ndef sat(x: float, a=7987622700):\\n    return abs(x ** 2 - a) < 10 ** -3\\nI have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\\nPlease follow the logical sequence of our subtasks to solve this problem.'}, {'role': 'user', 'content': '\\nSo far, the answers to the resolved sub-tasks are as follows: The format is SubtaskId: xxx; Subtask: xxx; Answer: xxx.\\nSubtaskId: 4; Subtask:  Recall mathematical knowledge: \\'x\\' is essentially the square root of \\'a\\', within a small tolerance. ; Answer: Given that \\'x\\' is essentially the square root of \\'a\\' within a small tolerance, to find an appropriate \\'x\\', one needs to calculate the square root of \\'a\\' (7987622700) and ensure the result is precise to within a very small margin, specifically less than 10^-3..\\nSubtaskId: 1; Subtask:  Understand the objective: Find a float \\'x\\' such that the difference between \\'x\\' squared and \\'a\\' is less than 0.001. ; Answer: Based on the insights provided from SubtaskId: 4, solving for \\'x\\' involves calculating the square root of \\'a\\' with a very high precision. The given value of \\'a\\' is 7987622700. \\n\\nTo find a float \\'x\\' such that the difference between \\\\(x^2\\\\) and \\'a\\' is less than \\\\(0.001\\\\), we aim to calculate the square root of \\'a\\'. Essentially, we\\'re seeking to identify \\\\(\\\\sqrt{7987622700}\\\\) with a precision that when squared, the absolute difference from 7987622700 is less than \\\\(10^{-3}\\\\).\\n\\nTo calculate this:\\n\\n\\\\[x = \\\\sqrt{a} = \\\\sqrt{7987622700}\\\\]\\n\\nHigh precision calculation tools or programming languages functions that handle floating-point arithmetic with significant precision are required to ensure the difference criterion (\\\\(< 10^{-3}\\\\)) is met.\\n\\nEmploying Python for this calculation as an example:\\n\\n```python\\nimport math\\nx = math.sqrt(7987622700)\\n```\\n\\nThis calculation yields the value for \\'x\\' we are looking for, ensuring it meets the specified tolerance when squared and compared to \\'a\\'. Given the constraints outlined, it essentially means finding the square root of 7987622700 with a precision that ensures when \\'x\\' is squared, it is within the range \\\\([7987622699.999, 7987622700.001]\\\\).\\n\\nThus, calculating \\\\(\\\\sqrt{7987622700}\\\\) directly provides the solution to finding such an \\'x\\' and concludes the logical follow-through based on the insights from the subtasks..\\nSubtaskId: 2; Subtask:  Recognize input \\'a\\' is given and fixed. ; Answer: To proceed with solving the provided puzzle programmatically, we use the Python code snippet from the discussion:\\n\\n```python\\nimport math\\n\\n# Calculation based on the provided logic\\na = 7987622700\\nx = math.sqrt(a)\\n\\n# Verify if the solution meets the criteria\\nsolution = abs(x ** 2 - a) < 10 ** -3\\n\\nprint(\"The solution is:\", x)\\nprint(\"Does the solution meet the criteria?\", solution)\\n```\\n\\nBy executing the Python code snippet, you calculate the square root of \\\\(7987622700\\\\) and verify if squaring this calculated value of \\'x\\' and comparing it to \\'a\\' falls within the specified tolerance (\\\\(< 0.001\\\\)). This direct application of calculating the square root as the solution to finding \\'x\\' addresses the requirement set forth by the puzzle within the constraints of precision mentioned. Given this approach, the printed output will indicate the value of \\'x\\' that solves the puzzle, alongside a boolean confirmation indicating whether or not the solution criteria have been met..\\nSubtaskId: 3; Subtask:  Comprehend the condition to satisfy: abs(x ** 2 - a) < 10 ** -3. ; Answer: With the information gathered from the previous subtasks, we understand that the primary goal is to find a value of `x` such that the absolute difference between `x` ** 2 and `a` is less than 0.001. The value `a` is given as 7987622700. Based on the mathematical and programming insights gained:\\n\\n1. The formula to find the suitable `x` boils down to calculating the square root of `a`, given the close approximation within a small tolerance (\\\\(<10^{-3}\\\\)).\\n2. The calculated square root value of `a` needs to ensure that the squared result, when compared to `a`, fits within the tolerance specified.\\n\\nFollowing the steps outlined in the previous subtasks, `x` can be found using a square root function, preferably through a high-precision method or tool, such as Python\\'s `math.sqrt` function. The solution from SubtaskId: 2 provides a practical blueprint for implementing this calculation and verifying the absolute difference criterion:\\n\\n```python\\nimport math\\n\\n# Calculation based on the provided logic\\na = 7987622700\\nx = math.sqrt(a)\\n\\n# Verify if the solution meets the criteria\\nsolution = abs(x ** 2 - a) < 10 ** -3\\n\\nprint(\"The solution is:\", x)\\nprint(\"Does the solution meet the criteria?\", solution)\\n```\\n\\nWhen this code is executed,\\n\\n- It will calculate `x` as the square root of `a`, which directly addresses the given challenge.\\n- It will then verify if this solution (`x`) meets the specific requirement: whether squaring this value (`x` squared) and then checking the absolute difference from `a` results in a value less than 0.001.\\n\\nGiven that this calculation process and the subsequent verification align with the task\\'s requirements, executing this code directly leads us to the solution, fulfilling the set criterion of `abs(x ** 2 - a) < 10 ** -3`. This comprehensive approach encapsulates the exploration and insights gathered from the previous subtasks, concluding the logical progression set out from the initial comprehension to the final implementation stage..\\nAmong them, sub-tasks [2, 4] are directly related to this sub-task, so please pay special attention to them. Devise a strategy: Compute the square root of \\'a\\' as a starting point. '}]\n",
      "Answer: Given the analysis from the previous subtasks, especially emphasizing sub-tasks [2, 4], the clear strategy to solve this programming puzzle is to compute the square root of 'a' directly. The value of 'a' has been provided as 7987622700. Recalling the objective, which focuses on the precision of the calculation to ensure the squared result of 'x' is within a tiny margin (less than 0.001) of 'a', the direct calculation of the square root of 'a' would yield an 'x' that satisfies the condition specified in the puzzle.\n",
      "\n",
      "To implement this strategy programmatically, Python's `math.sqrt` function has been identified as a suitable tool for performing high-precision square root calculations. This approach guarantees that the calculated 'x' will closely approximate the square root of 'a', meeting the condition `abs(x ** 2 - a) < 10 ** -3`.\n",
      "\n",
      "As detailed in SubtaskId: 2:\n",
      "\n",
      "```python\n",
      "import math\n",
      "\n",
      "# Calculate square root of 'a' to get 'x'\n",
      "a = 7987622700\n",
      "x = math.sqrt(a)\n",
      "\n",
      "# The calculated 'x' is expected to satisfy the puzzle condition\n",
      "```\n",
      "\n",
      "This Python code snippet is a direct implementation of our strategy, leveraging the insights upon recognizing 'a' is fixed and understanding that 'x' represents the square root of 'a', within the tolerance specified. Hence, upon executing this code, the 'x' thus obtained is the solution to the programming puzzle, confirming the strategy derived from the discussion and analysis in all previous subtasks.\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append('C:\\\\Users\\\\Pluto\\\\Desktop\\\\TaDe')\n",
    "from utils import search_Predecessors\n",
    "\n",
    "\n",
    "heights = list(depths.keys())\n",
    "  # print(heights)\n",
    "MAXHeight = max(heights)\n",
    "# print(MAXHeight)\n",
    "answerDict = {}  # 只有已经做过回答的subtask才会被放到这里面来\n",
    "\n",
    "\n",
    "for i in range(MAXHeight):\n",
    "    subtasks = depths[i]\n",
    "    for subtaskid in subtasks:\n",
    "        \n",
    "        number = re.findall(r'\\d+', subtaskid)\n",
    "        number = int(number[0]) if number else None\n",
    "        subtask = steps_dict[number]\n",
    "        \n",
    "        # question 问题字符串\n",
    "        # 交待解决任务\n",
    "        sys_q = f\"\"\"You will be provided with a Programming Puzzle. Your task is to find an input that will make the program return True.\n",
    "Here is the puzzle:\\n{question}\n",
    "I have broken this puzzle down into many easier subtasks. I will assign you sub-tasks one by one, and provide the results of the previous sub-tasks as a reference for your reasoning.\n",
    "Please follow the logical sequence of our subtasks to solve this problem.\"\"\"\n",
    "        \n",
    "        if len(answerDict)>0:\n",
    "          answersSoFar = f\"\"\"\\nSo far, the answers to the resolved sub-tasks are as follows: The format is SubtaskId: xxx; Subtask: xxx; Answer: xxx.\"\"\"\n",
    "          for key, value in answerDict.items():\n",
    "            answersSoFar += f\"\"\"\\nSubtaskId: {key}; Subtask: {answerDict[key]['subtask']}; Answer: {answerDict[key]['answer']}.\"\"\"\n",
    "            \n",
    "          predecessors = search_Predecessors(int_edges, number)\n",
    "          intersection = set(answerDict.keys()).intersection(set(predecessors))\n",
    "          count = len(intersection)\n",
    "          if count>0:\n",
    "            answersSoFar += f\"\"\"\\nAmong them, sub-tasks {predecessors} are directly related to this sub-task, so please pay special attention to them.\"\"\"\n",
    "        \n",
    "          \n",
    "        subask = f\"\"\"\\nNow the subtask is: {subtask}\n",
    "Based on the information above, please provide a concise and clear answer to this sub-task in one or two sentences..\"\"\"\n",
    "\n",
    "        if len(answerDict)>0:\n",
    "          query = answersSoFar+subtask\n",
    "        else:\n",
    "          query = subask\n",
    "\n",
    "        Q = [\n",
    "          {'role':'system', 'content':sys_q},\n",
    "          {'role':'user', 'content':query},\n",
    "        ]\n",
    "              \n",
    "        # print(subtaskid)\n",
    "        # print(subtask)\n",
    "        print('**********Question**********')\n",
    "        print(Q)\n",
    "        result = askChatGPT(Q, model=GPT_MODEL, temperature=1)\n",
    "        print('Answer:', result)\n",
    "        print('\\n\\n\\n')\n",
    "        \n",
    "        answerDict[number] = {'subtask':subtask, 'answer':result}\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\"89373.5533904092\"\n"
     ]
    }
   ],
   "source": [
    " # 已经问完了所有的subtask,最后问一次得到最终的答案\n",
    "Q.append({'role':'assistant', 'content':result})\n",
    "Q.append({'role':'user', 'content':\"\"\"Now that all the sub-tasks have been completed, so what is the correct input?\n",
    "Please give the input in the format of a string and just give the answer without any additional explanation or clarification.\"\"\"})\n",
    "finalResult = askChatGPT(Q, model=GPT_MODEL, temperature=1)\n",
    "print(finalResult)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for ** or pow(): 'str' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[122], line 38\u001b[0m\n\u001b[0;32m     34\u001b[0m exec(question)\n\u001b[0;32m     36\u001b[0m converted_result \u001b[39m=\u001b[39m convert_to_type(puzzles[i][\u001b[39m'\u001b[39m\u001b[39mans_type\u001b[39m\u001b[39m'\u001b[39m], finalResult)\n\u001b[1;32m---> 38\u001b[0m result \u001b[39m=\u001b[39m sat(converted_result)\n\u001b[0;32m     39\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39m\"\u001b[39m\u001b[39m函数运行结果为：\u001b[39m\u001b[39m\"\u001b[39m, result)\n\u001b[0;32m     40\u001b[0m \u001b[39mprint\u001b[39m(result \u001b[39m==\u001b[39m \u001b[39mTrue\u001b[39;00m)\n",
      "File \u001b[1;32m<string>:2\u001b[0m, in \u001b[0;36msat\u001b[1;34m(x, a)\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for ** or pow(): 'str' and 'int'"
     ]
    }
   ],
   "source": [
    "# 执行字符串形式的代码，使其在当前命名空间中定义函数\n",
    "# 定义类型字典\n",
    "from typing import Any, List\n",
    "type_dict = {\n",
    "    'str': str,\n",
    "    'int': int,\n",
    "    'float': float,\n",
    "    'bool': bool,\n",
    "    'List[int]': List[int],\n",
    "    'List[str]': List[str],\n",
    "    'List[float]': List[float],\n",
    "    'List[bool]': List[bool],\n",
    "    'List[List[int]]': List[List[int]],\n",
    "    'List[List[float]]': List[List[float]],\n",
    "    'List[List[str]]': List[List[str]],\n",
    "    'List[List[List[int]]]': List[List[List[int]]]\n",
    "}\n",
    "# 根据ans_type_str将结果转换为相应的类型\n",
    "def convert_to_type(type_str: str, value_str: str) -> Any:\n",
    "    \"\"\"\n",
    "    根据给定的类型字符串和待转换的字符串,将其转换为相应的Python类型\n",
    "    \"\"\"\n",
    "    if type_str in type_dict:\n",
    "        python_type = type_dict[type_str]\n",
    "        if type_str.startswith('List'):\n",
    "            # 处理列表类型\n",
    "            return eval(value_str)\n",
    "        else:\n",
    "            # 处理基本类型\n",
    "            return python_type(value_str)\n",
    "    else:\n",
    "        raise ValueError(f\"不支持的类型: {type_str}\")\n",
    "\n",
    "exec(question)\n",
    "\n",
    "converted_result = convert_to_type(puzzles[i]['ans_type'], finalResult)\n",
    "\n",
    "result = sat(converted_result)\n",
    "print(\"函数运行结果为：\", result)\n",
    "print(result == True)"
   ]
  }
 ],
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